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Effect of Non-Drag Forces on the Numerical Simulation of

Bubbly Flow in a Bubble Column

Wu Qian, Wang Xue-kui, Sha Zuo-liang*

Tianjin Key Laboratory of Marine Resources and Chemistry, Tianjin University of

Science and Technology

College of Marine Science and Engineering, Tianjin University of Science and

Technology, No. 29, 13th. Avenue, TEDA, Tianjin, China 300457, zsha@tust.edu.cn

Accuracy of CFD simulation on the bubbly flow was investigated by considering

different kinds of non-drag forces in a flat bubble column aerated from a single-orifice

gas sparger by comparison with the experimental data presented by Pfleger et al. (1999).

The simulated results reveal that the lift force model does not have significant effect,

while the turbulent dispersion force model can give much better results.

1. Introduction

Bubble columns, as one of the most efficient multiphase reactors, are used in many

important industrial fields. This is due to the simple construction, low operating costs

and high transfer efficiency (Kulkarni et al., 2007). However, the hydrodynamics in the

bubble column are affected by many factors and difficult to be described accurately.

CFD is considered as a powerful tool to study the bubbly flow in the bubble column.

It is well-known that the bubble plume is a flow characteristic in a locally aerated flat

bubble column. This phenomenon was simulated well by CFD and qualitatively proved

with the experimental data (Becker et al., 1994). Sokolichin et al. (1999) have studied

the applicability of closure models on the simulation. But non-drag forces were usually

ignored in the previous works. Recently, it was reported that the drag force alone would

not be sufficient to predict the local hydrodynamics correctly (Daz et al., 2008) and the

proper selection and description of non-drag forces are also of prime importance.

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The aim of this work was to make an attempt to present a sensitivity analysis of

different kinds of non-drag forces including the liftforce and turbulent dispersion force.

Effects of non-drag forces on the numerical simulation of bubbly flow hydrodynamics

were simulated in a 2D flat bubble column equipped with a single-orifice gas sparger.

The simulations were carried out based on two-phase fluid model.

2. Govern equations and models

Based on Euler-Euler approach, the momentum equation could be expressed as:

,( ) ( ) ( ( ( ) ))Tk k k k k k k k k k k k k m k k pt

+ = + + + +

u u u u u F g (1)

Fk,mis the interphase force described by Olmos et al. (2003). Drag force was modeled

as proposed by Clift et al. (1978) and the wall lubrication coefficient was set to 0.1.

Lift force with coefficient was given by following equation (Tomiyama et al., 1999):

, ,( )LF LF

l g g l L g l g l lC = = F F u u u

(2)Turbulent dispersion force was calculated by the model from Bertodano et al. (1991):

, ,

TD TD

l g g l TD l gC k = = F F (3)

CTDis the turbulent dispersion coefficient with recommended value of 0.1.

As reported by Lucas et al. (2001), there was a fluctuating motion of single bubble

caused by deformation, which increased with the Etvs number. It brought an

additional smoothing for the radial distribution of gas holdup, which was not covered byEq. (3). For this reason a second dispersion force was introduced and modeled as:

( ), ,, , , 1TD Eo TD Eo

l g g l TD Eo l d gC Eo = = F F (4)

According to the literature, CTD,Eowas 0.0015 m2 s

2forEod>1 and zero forEod

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3. Computation Setup

In order to compare with the experimental results obtained by Pfleger et al., (1999), the

numerical simulations were carried out in a 2D air-water flat bubble column with a

rectangular cross-section (0.2 m0.45 m0.04 m). Gas was introduced through a

single-orifice gas sparger, in the centre of which located a hole with diameter of 1 mm.

The whole transient simulations were done with the superficial gas velocity of 0.3 m/s.

Fig. 1 Geometry and mesh configurations of two-dimensional flat bubble column

Commercial software CFX 4.4 was used. The walls of bubble column were set to

no-slip boundary. Degassing boundary was used for the outlet surface. The average

bubble size was set to 2 mm. A uniform grid having 6060 cells and a time step of

0.001 s were used in all simulations, which were proved to give satisfactory results.

4. Simulated Results and Discussion

4.1 Effect of lift force model

The simulated distributions of gas holdup with and without lift force model are given in

Fig. 2-a. It can be qualitatively seen that the simulated flow states are similar to the

visual observation by Pfleger. As shown in Fig. 2-b, vortical eddies caused by bubble

plume and descending liquid flow along the sidewalls of bubble column are found,

which also agree with the experiment. The simulated results are almost independent on

the addition of lift force model except enlarging the amplitude of bubble plume.

Fig. 3 shows the computational results monitored at h=0.3 m. It is found that the lift

force affects the radial distribution of gas holdup and liquid velocity clearly. Bubbles

gather at the center of bubble column and the radial profile is approximately

axisymmetric without the lift force model. With adding the model, it seems that bubbles

are driven away from the axis and spread over the cross section of bubble column.

OUTLET

4

5cm

Y

XZ

4 cm

20 cmINLET

1 mm

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a. Gas holdup No FLF Add FLF Experiment (Pfleger et al., 1999)

b. Liquid velocity No FLF Add FLF

Fig. 2 Effect of lift force model on the simulation of bubbly flow

The peak of gas holdup moves to the left as seen in Fig. 3-a. The reason is that the

smaller bubbles tend to transfer to the walls of column under the action of lift force. Fig.

3-b presents that the simulated liquid vertical velocity agree well with the experimental

data and show a qualitatively correct of fluid circulation in the experimental condition.

As a result, the lift force model used here has no significant effect on simulating the

bubble plume in a single-orifice bubble column, which agrees with Daz et al. (2008).

0.00 0.05 0.10 0.15 0.20

0.00

0.05

0.10

g

Column Width, m

No FLF

Add FLF

0.00 0.05 0.10 0.15 0.20

-0.1

0.0

0.1

0.2

-0.2

0.0

0.2

0.4

Experimental data (Pfleger, 1999)

Simulated results with FTD

(Ug=0.17 cm/s)

LiquidVerticalVelocity,m/s

Column Width, m

NoFLF

AddFLF

a. Gas holdup radial distribution b. Liquid velocity radial distribution

Fig. 3 Effect of lift force model on the radial profile of hydrodynamic parameters

4.2 Effect of turbulent dispersion force model

It can be seen intuitively that bubbles move upwards directly and do not show the

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distinct horizontal swing without the turbulent dispersion force as shown in Fig. 4.

a. Gas holdup No FTD Add FTD Add FTDwith FTD,Eo

b. Liquid velocity No FTD Add FTD Add FTDwith FTD,Eo

Fig. 4 Effect of turbulent dispersion force model on the simulation of bubbly flow

Contrarily, with the consideration of turbulent dispersion force, the fluid dynamic

movement is similar to the experimental observation and takes on the clear bubble

plume. This may be explained by the action of turbulent dispersion force for distributing

the bubbles over the cross section. However, it is found that the additional dispersion

force model given by Lucas et al. (2001) do not bring significant change here.

0.00 0.05 0.10 0.15 0.20

0.00

0.05

0.10

0.15

0.20

g

Column Width, m

No FTD

Add FTD

Add FTD

+FTD,EO

0.00 0.05 0.10 0.15 0.20

-0.1

0.0

0.1

0.2

-0.2

0.0

0.2

0.4

LiquidVerticalVelocity,m/s

Column Width, m

Experimental data (Pfleger, 1999)

Simulated results with FTD

(Ug=0.17 cm/s)

NoFTD

AddFTD

AddFTD

+FTD,EO

a. gas holdup radial distribution b. liquid velocity radial distribution

Fig. 5 Effect of turbulent dispersion force model on the hydrodynamic parameters

As shown in Fig. 5, the radial profile of gas holdup becomes flatter with the

consideration of turbulent dispersion force model than without that. The peak of liquid

vertical velocity moves leftward, while with the additional dispersion force both curves

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only move to the left appreciably. It can be attributed to the fluctuating movement of

bubbles and the turbulent dispersion force prevents bubbles accumulating within a small

region close to the centerline. Due to the additional dispersion force mainly acts on the

larger bubbles (db6 mm) pointed by Lucas et al. (2001), the obvious change can not

be found with the average bubble diameter of 2 mm in the present work.

5. Conclusion

Effects of non-drag forces (lift and turbulent dispersion) on the simulation of bubbly

flow in a centrally aerated flat gas-liquid bubble column were investigated. It reveals

that the additions of lift and additional dispersion force model do not have significanteffect, while the turbulent dispersion force model can give much better results.

References

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